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A008811 Expansion of x*(1+x^4)/((1-x)^2*(1-x^4)). 10
0, 1, 2, 3, 4, 7, 10, 13, 16, 21, 26, 31, 36, 43, 50, 57, 64, 73, 82, 91, 100, 111, 122, 133, 144, 157, 170, 183, 196, 211, 226, 241, 256, 273, 290, 307, 324, 343, 362, 381, 400, 421, 442, 463, 484, 507, 530, 553, 576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of 0..n-1 arrays of 5 elements with zero 2nd differences. - R. H. Hardin, Nov 15 2011

REFERENCES

Pach and Agarwal, Combinatorial Geometry, p. 220, Problem 13.10.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

FORMULA

G.f.: x*(1+x^4)/((1-x)^2*(1-x^4)).

a(n) = 2*a(n-1) -a(n-2) +a(n-4) -2*a(n-5) +a(n-6). - R. H. Hardin, Nov 15 2011

a(n) = (-2*(1+(-1)^n)*(-1)^floor(n/2) + 2*n^2 + 5 - (-1)^n)/8. - Tani Akinari, Jul 24 2013

MAPLE

f := n->n^2/4+3*n/2+g(n);

g := n->if n mod 2 = 0 then 3 elif n mod 4 = 1 then 9/4 else 13/4; fi;

seq(f(n), n=-3..50);

MATHEMATICA

CoefficientList[Series[x*(1+x^4)/((1-x)^2*(1-x^4)), {x, 0, 60}], x] (* G. C. Greubel, Sep 12 2019 *)

PROG

(PARI) concat([0], Vec(x*(1+x^4)/((1-x)^2*(1-x^4))+O(x^60))) \\ Charles R Greathouse IV, Sep 26 2012, modified by G. C. Greubel, Sep 12 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); [0] cat Coefficients(R!( x*(1+x^4)/((1-x)^2*(1-x^4)) )); // G. C. Greubel, Sep 12 2019

(Sage)

def A008811_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P(x*(1+x^4)/((1-x)^2*(1-x^4))).list()

A008811_list(60) # G. C. Greubel, Sep 12 2019

(GAP) a:=[0, 1, 2, 3, 4, 7];; for n in [7..60] do a[n]:=2*a[n-1]-a[n-2] +a[n-4]-2*a[n-5]+a[n-6]; od; a; # G. C. Greubel, Sep 12 2019

CROSSREFS

Cf. A129756 (first differences).

Cf. Expansions of the form (1+x^m)/((1-x)^2*(1-x^m)): A000290 (m=1), A000982 (m=2), A008810 (m=3), this sequence (m=4), A008812 (m=5), A008813 (m=6), A008814 (m=7), A008815 (m=8), A008816 (m=9), A008817 (m=10).

Sequence in context: A073627 A062042 A107817 * A144678 A309678 A279225

Adjacent sequences:  A008808 A008809 A008810 * A008812 A008813 A008814

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 7 20:29 EST 2019. Contains 329849 sequences. (Running on oeis4.)